If I put a 30db distribution amplifier on the coax, then run it through a 1 to 2 splitter, what is the approximate signal reduction, just 3db off the 30 db amplification?
30 minus 3 = 27db?
I had read a splitter reduces signal by 50%, so then I was thinking it could be 30 minus 15 = 15?

27dBmV is 50% less than 30dBmV, but that isn't what your going to have for signal levels. A 30dB gain amplifier increases the signal strength by 30dB. If it was 10 dBmV before it went into the amplifier, then it would be 40 dBmV coming out.

Rarely does a residential situation need or benefit from 30dB of amplification. What is your situation? What is your TV signal source, how many TVs is your system supporting, and how long ar the coax wiring runs?

FYI: A 2-way RF Splitter results in the output signals being not quite 50% of the input power.....which in DECIBELS, is 3 dB loss on each port....plus internal losses of about 0.5 to 1 dB, for a total loss of about 3-4 dB per port:http://en.wikipedia.org/wiki/Decibel

An Amplifier improves Sensitivity by reducing the Post-Preamp Noise Figure by the Inverse of the Scalar Gain, which is the sum of the Splitter + Cable Losses + Tuner Noise Figure (typ 5-10 dB). Hence System Losses of say 20 dB are reduced to an "adequate" 0.63 dB by an Amplifier with a Scalar Gain of 32 (15 dB) and are reduced to an OVERKILL of 0.02 dB by an Amplifier with a Scalar Gain of 1000 (30 dB). But high Gain Preamps make the system much more susceptible to Intermodulation Distortion due to strong (and sometimes moderate) input signal levels, greatly reducing their Sensitivity to weak station reception.

On the boat, I noticed 53 sometimes breaks up.
I currently have an amp of 12db with a range from 50 to 450mhz.
I dont like the fact does not amp to the whole TV freq spectrum.
So I got an amp made by cabletronics, 30db with adjustment screw and range of 50 to 1000mhz for $20.

An easy analogy of a splitter is to think of a water pipe with one input and 2 outputs (if both outputs are equal) you will get half of the water flow through one output and half through the 2nd output,
A 2 way balanced splitter (or power divider) does the same thing as stated when you express half power it is a 3db reduction in level..

You can use the same analogy for any number of outputs, however keep in mind that this is through a perfect splitter (these don't exist) , there are other factors that occur which are part of the equation so this is all theoretical.

A 30db gain amp is probably to high for typical residential application, and will likely overload and be detrimental to reception. And a 4db noise figure is a bit high. A 15db amp from Channel Master would likely be better, and they also have 2, 4, and 8-port versions.

Yes, you can add & subtract dB levels....for example to determine signal level at input to HDTV Tuner (Sih) for TVFool RX(dbm) prediction, in case you want to know how much signal margin you have above typical Tuner Sensitivity of say -85 to -80 dBm:

For good TV reception you have to get away from idea that Higher Gain is somehow better and concentrate on reducing the System Noise Figure (to improve Sensitivity) while also Maximizing Spurious Free Dynamic Range (SFDR, search forum for my posts on this subject) by choosing a Preamp with the "right" combination of Overload resistance and just enough Gain to reduce System NF without generating excessive Intermod Distortion.

I also have a Spread Sheet to conduct Overload Calculations and select a Preamp that Maximizes SFDR (if you can figure it out):http://photos.imageevent.com/holl_ands/files/ota/icons/DTV%20Preamp%20Signal%20Overload%20Calculator%20-%20RevM.xls.jpg
Note that if your Preamp does not appear in the Spread Sheet it is because the manufacturer does not advertise meaningful Overload specs, which must include the number and (input or output) signal levels of the 2 or more strong signals tested and (most importantly) what the Intermod or "Crossmod" noise level is for the given input test condition (C-M and W-G use 46 dB Crossmod spec and Europe uses several different DIN tests). Most good Preamps will have separate specs for their independent VHF and UHF Amplifier strips....a single common Amplifier means UHF will probably be degraded by strong FM signals that a simple Notch Filter is ineffective at suppressing....indeed, in most cases I recommend trying VHF Reception WITHOUT ANY Amplification to avoid this and other related issues.

I installed into boat today and wow, works very well.
Works so well I do not even need a VHF antenna, which I do not understand?
VHF did not work with the 12db amp and no vhf antenna.

I have now vhf square loop antenna and uhf double bow tie antenna.
I disconnected my balun cause it needs solder repair. And channel 4.1 still works?
4.1 = 9, 13.1 = 13, 21.1 = 7 and all work perfect without hooking up and work perfect with hooking up to the vhf loop.

One reason I got this amp is channel 4.1 was breaking up badly on the 12db amp and using the FM antenna for VHF, all other VHF worked great on the FM antenna. 4.1 channel is over 40 miles away. Zipcode 23608 is location of house. Boat is around 23669 zip.

Pictures
uhf bowtie
FM radio
vhf loop

The gemini uhf-vhf-fm splitter thing at my house did block the VHF when I hooked up my bowtie antenna as a test
And passed VHF and not uhf when attached to my house antenna as a test.
Boat is 10 miles closer to towers.
Could the signal somehow with all the metal underthere resonate into the coax or say the UHF antenna and the 30db amp has enough power to make it work?

Simple UHF 4-Whisker Bowtie has as much Raw Gain as the Loop in most Rabbit-Ear Antennas....but SWR is Excessive, which may or may NOT be a problem, depending on cable length and signal strength:http://imageevent.com/holl_ands/dipoles/uhfbowties
Loop optimized for Hi-VHF (as used in your boat) will have somewhat higher Raw Gain with good SWR.

I like the idea of improving on the bowtie by adding in wires.
Your solid bowtie example has tine separations of 12".
I don't think there is enough room inside the cabinet to do that.
My bowtie is 9.5" long whiskers by 9 " between the bows measured at the feed line wires. (bow separation)
My tine separation I did not measure. Likely about 7 to 8".

Would the effect of filling in the area with some copper wire as shown in the pictures be a good idea?
I assume the particular pattern is less important or is it?
How about enclosing the tine ends, then wrapping a long strand of thinner copper wire around the tines and soldering the wire intersections. Keep wrapping down to the feed line wires. Maybe with a inch spacing?